68 



STATICS OF SYSTEMS OF PARTICLES 



100 tf> s - 



FIG. 35 



2. The nutcracker. It is found that a weight of 100 pounds placed on top of a 

 nut will just crack it. How much force must be applied at the ends of the arms of 

 a nutcracker 6 inches long to crack the nut when it is placed | inch from the hinge ? 



Let a force F applied at the extreme end of each arm be supposed just suffi- 

 cient to crack the nut. Then when a force F is applied at the end of the arm, the 

 pressure between the nut and the arm must be the weight of 100 pounds. Thus 



the forces acting from outside on either arm 

 of the nutcracker will consist of 



(a) the force F applied at the end of the arm ; 

 (6) the pressure of 100 pounds weight exerted 

 by the nut on the arm at a distance of i inch 

 from the hinge ; 



(c) the reaction at the hinge. 

 The weight of the nutcracker is here supposed 

 to be negligible. 



Taking moments about the hinge, we obtain 



6 x F = i x 100 pounds weight, 

 so that F = 8| pounds weight. 



NOTE. When, as here, au unknown force neither enters in the data nor is required 

 in the answer, we can always obtain equations in which the force does not occur, by 

 taking moments about a point in its line of action. So again, if two such forces occur, 

 we can obtain an equation into which neither force enters, by taking moments about 

 the point of intersection of their two lines of action. 



3. A ladder stands on a rough horizontal plane, laining against a rough ver- 

 tical wall, the contacts at the two ends of the 



ladder being equally rough. Find how far a 

 man can ascend the ladder without its slipping, 

 it being supposed that the weight of the ladder 

 may be neglected. 



The forces acting on the system composed 

 of the man and ladder are three in number : 

 (a) the reaction with the horizontal plane ; 

 (6) the reaction with the vertical wall ; 

 (c) the weight of the man. 



These forces are all in one plane ; hence, 

 by the theorem of 52, their lines of action 

 must meet in a point. 



In the figure let AB be the ladder, C 



the position of the man, and P the point in 



which the three forces meet, so that PC is A 



vertical, and AP, BP are the lines of action FlG - 36 



of the reactions at A, B. When slipping is just about to begin, each of these 



reactions must make with the normal an angle equal to the angle of friction. 



